Taper shapes for sidelobe suppression and bandwidth minimization in distributed feedback optical reflection filters

Abstract

Improvements in distributed feedback optical reflection filters are described. In particular, taper shapes for the optical reflection couplers are determined by a design method based on a variational optimization theory, to provide an out-of-band sidelobe suppression ratio of greater than -30 dB, and a reduced width of the filtered bandwidth for a specified side lobe suppression level. These filter characteristics were determined by specifying the interaction strength reflection function along the length of the coupler, by the design formulaKS(z)=Lo(z)+SL1(z)+S2L2(z)+S3L3(z)where KS(z) is the interaction strength; S is the desired sidelobe level in |dB| Li(z) (i=0,1,2,3) are functions of the propagation distance z. The functions Li(z) are given by: <IMAGE> where Lc is the physical length of the coupler, and the set of constant coefficients bi,j are given by: - j - bi,j 1 2 3 4 - b0,j 1.316 -0.4430 2.839e-1 -1.902e-1 - b1,j 1.308e-2 1.906e-2 -1.778e-2 1.229e-2 - b2,j -1.540e-4 -1.136e-4 2.736e-4 -2.359e-4 - b3,j 7.10e-7 1.541e-7 -1.397e-6 1.414e-6 - j - bi,j 5 6 - b0,j 1.337e-1 -9.33e-2 - b1,j -8.188e-3 5.436e-3 - b2,j 1.615e-4 -1.048e-4 - b3,j 1.0279e-6 6.680e-7 - In practice, the specified interaction strength is produced by modulating one of the physical parameters of the DFB filter for example, the vertical depth of horizontal width of corrugations of the reflection grating; the index contrast ratio; the duty cycle of the reflection grating; or by defining the on-off sample rate of the grating corrugations.

What is claimed is: 
     
       1. A distributed feedback optical reflection filter coupler wherein the interaction strength reflection function along the length z of the coupler, is specified by the design:   K.sub.S (z)=L.sub.o (z)+SL.sub.1 (z)+S.sup.2 L.sub.2 (z)+S.sup.3 L.sub.3 (z)     where K S  (z) is the normalized interaction strength along the propagation direction, S is the desired sidelobe level in |dB|, L i  (z) (i=0,1,2,3) are functions of the propagation distance z, and the functions L i  (z) are given by ##EQU11##  where L c  is the physical length of the coupler, and the set of constant coefficients b i ,j are given by   ______________________________________                                    
b.sub.i,j                                                                 
        1          2         3        4                                   
______________________________________                                    
b.sub.0,j                                                                 
        1.316     -0.4430    2.839e-1                                     
                                     -1.902e-1                            
b.sub.1,j                                                                 
        1.308e-2   1.906e-2 -1.778e-2                                     
                                      1.229e-2                            
b.sub.2,j                                                                 
       -1.540e-4  -1.136e-4  2.736e-4                                     
                                     -2.359e-4                            
b.sub.3,j                                                                 
        7.10e-7    1.541e-7 -1.397e-6                                     
                                      1.414e-6                            
______________________________________                                    
                    j                                                     
                 b.sub.i,j                                                
                       5         6                                        
______________________________________                                    
                 b.sub.0,j                                                
                       1.337e-1 -9.33e-2                                  
                 b.sub.1,j                                                
                      -8.188e-3  5.436e-3                                 
                 b.sub.2,j                                                
                       1.615e-4 -1.048e-4                                 
                 b.sub.3,j                                                
                       1.0279e-6                                          
                                 6.680e-7                                 
______________________________________                                    
       
     
     
       2. A DFB optical reflection filter coupler according to claim 1 wherein the filter comprises a reflection grating having a vertically corrugation depth, and the specified interaction strength K S  (z) is produced by modulation of the vertical corrugation depth of the reflection grating. 
     
     
       3. A DFB optical reflection filter coupler according to claim 1 wherein the filter comprises a reflection grating having a horizontal corrugation width, and the specified interaction strength K S  (z) is produced by modulation of the corrugation width of the reflection grating. 
     
     
       4. A DFB optical reflection filter coupler according to claim 1 wherein the filter comprises a reflection grating wherein the modulation of the duty cycle duty cycle provides the specified interaction strength K S  (z). 
     
     
       5. A DFB optical reflection filter coupler according to claim 1 comprising a grating with a on-off sample rate of the grating corrugations defined to provided the specified interaction strength K S  (z). 
     
     
       6. A DFB optical reflection filter coupler according to claim 1 comprising an index modulation grating having high index and low index regions, and wherein the modulation of the high and low index contrast provides the specified interaction strength K S  (z). 
     
     
       7. A distributed feedback optical reflection filter coupler comprising a grating structure, wherein a physical parameter of the grating structure is modulated along a propagation direction to define an interaction strength, and wherein the taper shapes determining the interaction strength as a function of propagation distance z along the length of the coupler are determined by the design   K.sub.S (z)=L.sub.o (z)+SL.sub.1 (z)+S.sup.2 L.sub.2 (z)+S.sup.3 L.sub.3 (z)     where   K S  (z) is the interaction strength as a function of the propagation distance z, S is the specified sidelobe level in |dB|, and   L o  (z) . . . L 3  (z) are functions of the propagation distance z, to provide an interaction strength reflection function having an out-of-band sidelobe suppression ratio of greater than -30 dB, and a minimum width of the filtered bandwidth for a specified side lobe suppression level.     
     
     
       8. The distributed feedback optical reflection filter coupler of claim 7, wherein the function L o  (z) to L 3  (z) are given by ##EQU12## where: L c  is the physical length of the coupler, z is the propagation distance along the coupler, and the set of coefficients b i ,j are optimized, to provide an interaction strength reflection function having an out-of-band sidelobe suppression ratio of greater than -30 dB, and a minimum width of the filtered bandwidth for a specified side lobe suppression level.